1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Upper bound and lower bound

  1. Aug 29, 2010 #1
    1. The problem statement, all variables and given/known data

    1.
    f(n) = n - 100
    g(n) = n - 200

    2.
    f(n) = log(2n)
    g(n) = log(3n)

    n >= 0 in all cases
    Find out if f(n) is an upperbound, lowerbound or both of g(n)
    2. Relevant equations



    3. The attempt at a solution

    in case of 1, f(n) has to be an upperbound of g(n) because when graphed together, f(n) has to be an upperbound of g(n).

    For 2, solution does not exist at n = 0. Otherwise, f(n) is a lower bound of g(n). Does this mean that f(n) is a lower bound or both?
     
  2. jcsd
  3. Aug 30, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Too vague. What you should say is "200> 100 so -100> -200 and n- 100> n- 200 for all n. Since f(n)> g(n) for all n, f is an upper bound of g."

    Is suspect that should not be "[itex]n\ge 0[/itex] for both cases" but only n> 0 for the second. As you point out, ln(0) is not defined so the problem makes no sense for n= 0.

    ln(2)< ln(3) so ln(n)+ ln(2)< ln(n)+ ln(3) for all n> 0. ln(2n)< ln(3n) for all n> 0.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook